Mon, May 4 3pm ET (8pm BST, 7am Tue NZST)
Nathan Bowler, Universität Hamburg
I’ll talk about a couple of classes of matroids which sit between frame and lifted-graphic matroids: the biased graphic matroids, which sit between these classes in a sense introduced by Zaslavsky, and the slightly better behaved quasi-graphic matroids, which were recently introduced by Geelen, Gerards and Whittle. I’ll give a very concrete combinatorial descriptions of the quasi-graphic matroids and use this to derive a fairly clean characterisation of the biased graphic matroids. I’ll discuss a topological construction giving some nontrivial examples of quasi-graphic matroids and raise the question of whether most examples are constructed in essentially this way.
Mon, April 27 3pm ET (8pm BST, 7am Tue NZST)
Dillon Mayhew, Victoria University of Wellington
Definability and non-definability for classes of matroids
Monadic second-order logic provides a bridge between the theory of computation and the structure of graphs and matroids. So it is natural to ask which classes can be characterised by a sentence in monadic second-order logic. In some sense this problem is uninteresting for graphs, since every minor-closed class can be defined in this way. But there are minor-closed classes of matroids that can not be defined in monadic second-order logic. This talk is going to discuss the boundary between definability and non-definability, with special reference to classes of gain-graphic matroids.
Thank you all for making last week’s talk such a success! James’ talk is available on YouTube here. We will be recording talks in the future too and posting them to the same channel.
Due to a number of scheduling conflicts with other seminars, we are moving the talks to Monday 3pm EST (same time, different day). The next talk by Dillon Mayhew will be on April 27.
Future talks will have a password following the same format as last week’s password. You may have already received an email from Peter explaining this. Otherwise, please email rose.mccarty ~at~ uwaterloo ~.~ ca for the password. Hope to see you next Monday!
We’re happy to announce that the online matroid theory seminar starts this week with a talk by James Oxley. We’ll be posting the details of each talk about a week beforehand. Please keep an eye out for these posts as we may need to do some schedule adjustment for talks after this week. Any changes will be reflected on the Talks page.
Thanks for your support as we figure out this new format. We’re happy to hear from you – please email rose.mccarty ~at~ uwaterloo ~.~ ca if you’d like to share any feedback.
Thurs, April 16 3pm ET (8pm BST, 7am Fri NZDT)
James Oxley, LSU
The binary matroids with no odd circuits of size exceeding five
It is well known that a graph has no odd cycles if and only if it is bipartite. In 1992, Maffray showed that a $2$-connected simple graph that has a triangle but no larger odd cycles is isomorphic to $K_4$ or can be obtained by gluing together a collection of triangles across a common edge. This talk will discuss extensions of these results to binary matroids. This is joint work with Carolyn Chun and Kristen Wetzler.